scholarly journals Ambarzumian-type Problems for Discrete Schrödinger Operators

2021 ◽  
Vol 15 (8) ◽  
Author(s):  
Burak Hatinoğlu ◽  
Jerik Eakins ◽  
William Frendreiss ◽  
Lucille Lamb ◽  
Sithija Manage ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Schrödinger Operator ◽  
Inverse Spectral Problem ◽  
Unique Determination ◽  
Schrodinger Operator ◽  
Real Constant ◽  
Discrete Schrödinger Operator ◽  
Various Boundary Conditions ◽  
Discrete Schrödinger Operators

AbstractWe discuss the problem of unique determination of the finite free discrete Schrödinger operator from its spectrum, also known as the Ambarzumian problem, with various boundary conditions, namely any real constant boundary condition at zero and Floquet boundary conditions of any angle. Then we prove the following Ambarzumian-type mixed inverse spectral problem: diagonal entries except the first and second ones and a set of two consecutive eigenvalues uniquely determine the finite free discrete Schrödinger operator.

scholarly journals Thermal impedance estimations by semi-derivatives and semi-integrals: 1-D semi-infinite cases

2013 ◽  
Vol 17 (2) ◽  
pp. 581-589 ◽  
Author(s):  
Jordan Hristov ◽  
Ganaoui El
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Boundary Conditions ◽  
Half Time ◽  
Thermal Impedance ◽  
Entire Domain ◽  
Various Boundary Conditions ◽  
Transient Thermal

Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances under various boundary conditions imposed at the interface (x=0). The approach is purely analytic and very effective because it uses only simple semi-derivatives (half-time) and semi-integrals and avoids development of entire domain solutions. 0x=

ON THE SPECTRAL AND SCATTERING THEORY OF THE SCHRÖDINGER OPERATOR WITH SURFACE POTENTIAL

2000 ◽  
Vol 12 (04) ◽  
pp. 561-573 ◽  
Author(s):  
AYHAM CHAHROUR ◽  
JAOUAD SAHBANI
Keyword(s):  
Continuous Spectrum ◽  
Surface Potential ◽  
Schrödinger Operator ◽  
Scattering Theory ◽  
Schrodinger Operator ◽  
Absolutely Continuous Spectrum ◽  
Discrete Schrödinger Operator ◽  
Absolutely Continuous ◽  
Spectral And Scattering Theory

We consider a discrete Schrödinger operator H=-Δ+V acting in ℓ2 (ℤd+1), with potential V supported by the subspace ℤd×{0}. We prove that σ (-Δ)=[-2 (d+1), 2(d+1)] is contained in the absolutely continuous spectrum of H. For this we develop a scattering theory for H. We emphasize the fact that this result applies to arbitrary potentials, so it depends on the structure of the problem rather than on a particular choice of the potential.

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